An Application of Mathieu Function Expansions to Hull Form Improvement

Abstract

Mathieu-function-expansion method is proposed for evaluating and improving performance of ship hull forms. Medium speed ships, the design Froude number somewhere between 0.20 and 0.25, are mainly discussed.The present method is based on minimum wave resistance theory (Maruo and Bessho, 1963) for infinite draft wall-sided ships. When the half breadth curve is expanded by Mathieu functions, the coefficient of the higher order term has by far the greater effect upon the value of the wave resistance than the coefficients of the lower order terms. Using this fact the performance of the ship hull form is evaluated from the standpoint of the wave resistance and the information, how to improve the ship hull form is gotton.The tank tests are carried out to verify it and the results show that the present method is very powerful for improvement of practical ship hull forms.